A videotape cassette contains two spools, each of radius rs, on which the tape is wound. As the tape unwinds from the first spool, it winds around the second spool. The tape moves at constant linear speed v past the heads between the spools. When all the tape is on the first spool, the tape has an outer radius rt. Let r represent the outer radius of the tape on the first spool at any instant while the tape is being played.
(a) Show that at any instant the angular speeds of the two spools are ώ1 = v/r and ώ 2 = v/(rs 2 ) rt + 2 ─ r 2)1/2
(b) Show that these expressions predict the correct maximum and minimum values for the angular speeds of the two spools.